5 years ago

carol is twice lorraine's age. in six years, the sum of their ages will be 30. how old is each now?

let carol's age be x and lorraine's, y.
now: x=2y or you can simply say carol's age is 2y while lorraine's is y.
in 6 years: (2y+6)+(y+6)=30
3y+12=30
3y=18
y=6
hence carol's age is 12, and lorraine's age is 6.